Quantitative comparison of large sets of geochronological data using multivariate analysis: a provenance study example from Australia

Geochimica et Cosmochimica Acta, Vol. 64, No. 9, pp. 1593–1616, 2000 Copyright © 2000 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/00 $20.00 ⫹ .00

Pergamon

PII S00167037(99)00388-9

Quantitative comparison of large sets of geochronological data using multivariate analysis: A provenance study example from Australia KEITH N. SIRCOMBE* Continental Geoscience Division, Geological Survey of Canada, Ottawa, Ontario K1A 0E8, Canada (Received February 3, 1999; accepted in revised form October 18, 1999)

Abstract—A variety of modern isotopic analytical techniques now allow the relatively rapid acquisition of large sets of geochronological data, particularly in provenance studies. Traditional interpretation of this type of data often relies on visual comparison techniques that are vulnerable to subjective bias and this problem becomes acute with increasingly large quantities of data. Multivariate techniques are presented in this article to objectively evaluate age components within the detrital zircon age data from 31 beach sand and sedimentary samples in Australia for provenance studies. Using the SHRIMP Ion Microprobe each sample typically contains 60 or more individual age measurements with a combined total of 2150 analyses. Principal components derived from the data set allow the construction of provenance models that are independent of expected age components. In this instance the principal components are interpreted in terms of existing knowledge about Australian geology, in particular the provenance relationship between “local” Phanerozoicaged and “exotic” late Proterozoic-aged protosources. Using principal components analysis this relationship is seen clearly and objectively in one diagram illustrating provenance evolution along the eastern coastline. Copyright © 2000 Elsevier Science Ltd 1. INTRODUCTION

2. GEOLOGICAL BACKGROUND

2.1. Geological History

Acquisition of relatively large sets of age data has become routine in a variety of modern geochronological techniques such as isotope dilution thermal ionization mass spectrometry (e.g., Davis et al., 1990; Gehrels and Dickinson, 1995); secondary ionization mass spectrometry (e.g., Dodson et al., 1988; Whitehouse et al., 1997), inductively coupled plasma mass spectrometry (e.g., Machado et al., 1996; Scott and Gauthier, 1996); fission track (e.g., Hurford et al., 1984; Brandon and Vance, 1992); 40Ar/39Ar dating (e.g., Dallmeyer and Takasu, 1992; Adams and Kelley, 1998); and electron microprobe dating (e.g., Suzuki and Adachi, 1991; Montel et al., 1996). These quantities of data are particularly valuable for tracing sedimentary provenance by using the individual ages of certain detrital minerals as a proxy for their protolith ages (e.g., Morton et al., 1996; Pell et al., 1997; Sircombe, 1999; Sircombe and Freeman, 1999). Comparison of such age data sets typically involves the plotting of histograms and simple visual comparison between plots or expected age distributions to infer correlations, traits, and trends (e.g., Pell et al., 1997; Adams and Kelley, 1998; Ireland et al., 1998). This approach may be vulnerable to subjective bias and is inadequate in situations involving several or more samples requiring comparison. This article presents work toward establishing a quantitative method for the description and comparison of age data using multivariate analysis techniques with a demonstration using detrital zircon age data from Australia. Because the isotopic analytical details of the data are not the focus of this article, full listings of isotopic data are given elsewhere (Sircombe, 1997, 1999; Sircombe and Freeman, 1999).

*Author to whom correspondence ([email protected]).

should

be

The eastern and western Australian coastlines have been major sources of industrial zircon, rutile, and monazite for several decades. Along the eastern coastline, it has long been noted that the mineralogy of the coastal sands did not match that of fluvial sands in rivers assumed to contribute sediment to the coast from the nearby hinterland. This led to speculation of a distal and Precambrian source for the heavy minerals seen on the eastern coast (Gardner, 1955; Whitworth, 1959; Connah, 1961; Hails, 1969; Colwell, 1982). However, with no viable protosource1 in eastern Australia to compare mineralogy, this speculation could not be tested by conventional heavy mineral analysis. A recent renewal of heavy mineral placer exploration spurred a modern investigation of this problem using the sensitive high resolution ion microprobe (SHRIMP) to obtain geochronological data (Sircombe, 1997). Any provenance study requires a preliminary understanding of potential protosources and to aid the discussion, a brief geological summary of Australia is included. The western-third of the Australian continent contains the Archean Yilgarn and Pilbara cratons consisting of gneisses, granites, and metasediments ranging in age from 3600 to 2600 Ma (Myers, 1993). These cratons were amalgamated by a series of Proterozoic orogens between 1300 and 900 Ma (Plumb, 1979). The nearest significant exposure of Precambrian rocks to the modern southeastern Australian coastline is ⬎750 km inland in the Broken Hill area. After Neoproterozoic rifting and uplift of the Del1 This article will follow the convention of Pell et al. (1997) where protosource is defined as the igneous or metamorphic unit in which a detrital mineral originally formed (using the prefix proto- in the meaning of the original Greek protos or first rather than the inferred meaning of primitive or undeveloped). In contrast, the term provenance also includes any intermediate sedimentary repositories.

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Fig. 1. Sample locations with generalised geologic structure of southeastern and western Australia (geology based on Palfreyman, 1984). Locations with circles indicate eastern coastal samples; square symbols indicate Murray Basin samples; upright triangles indicate Sydney Basin samples; upside-down triangles indicate Southeast Australian fluvial samples; diamonds indicate West Australian samples.

amerian Orogeny accompanied by the accumulation of a large turbidite sequence, the eastern-third of the Australian continent accreted through a series of Phanerozoic orogenies broadly grouped as the Lachlan and New England Orogens (e.g., Coney et al., 1990). This activity culminated in late Mesozoic and early Cenozoic fragmentation of the Gondwana supercontinent and creation of the modern Australian continent (Veevers, 1984). As the rifted margins subsided, continental shelf marine sediments accumulated subject to periodic disruption by glacially driven eustatic sea level change (Roy and Thom, 1991). The eastern continental shelf is relatively narrow, thus limiting the maximum thickness of Cenozoic sedimentary deposits to only 600 m (Roy and Thom, 1991) and aiding high energy incident waves prevailing from the southeast to drive a distinct northward littoral drift (Roy and Thom, 1981).

2.2. Sample Locations A series of detrital zircon samples were taken from five study areas in eastern and western Australia (Fig. 1). (1) The modern eastern coastline was the focus of attention, with some sites being used to test the resolution of the technique (e.g., a repeat sample from Aslings Beach). The Lorne beach sample from Victoria is strictly outside the littoral system defining the eastern coastline, but has been included for comparison because its potential provenance includes the Cretaceous Otway Basin, which may not be present on the eastern coast. All samples are from the modern beach face, except the Tomago Sands sample, which is from a relict Plio-Pliestocene Inner Barrier. (2) The Murray Basin is a broad, almost land-locked interior basin that developed coevally with the continental margins through the

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Cenozoic (Brown and Stephenson, 1991). The Murray Basin has been a subject of recent exploration interest because the heavy minerals in the basin are believed to have had a similar origin to those on the eastern coast by virtue of being on the western side of the Great Dividing Range (Williams, 1990). The samples are from the Plio-Pliestocene Loxton-Parilla Sands, which generally underlie Quaternary dunefields in the basin. (3) The Sydney Basin is the southern section of a foreland basin formed during the Mesozoic as the New England Orogen encroached upon the Lachlan Orogen (Scheibner, 1993). Because of the lack of a potential Precambrian protosource in southeastern Australia, the Sydney Basin was sampled to test it as a possible intermediate sedimentary repository. Samples were taken from a variety of stratigraphic levels in the basin spanning the Permian and Triassic. (4) Samples were also taken from ancient and modern fluvial sediments in southeastern Australia to examine the extent of provenance signatures through various stratigraphic levels. These samples include Devonian/Carboniferous fluvial sandstones at Bombala (Sircombe and McQueen, in press), Tertiary fluvial sediments at Tuross Head and Brooman (Spry et al., 1999), and modern fluvial sand at Halfway Flat on the Snowy River. (5) Finally, samples from heavy mineral deposits on the Western Australian coastline were also analyzed to further investigate the discovery that detrital rutile from both eastern and western coasts displayed remarkably similar detrital rutile age distributions despite markedly different geological settings (M. C. Fanning et al., personal communication; Sircombe and Freeman, 1999). Three additional zircon age distributions from southeast Australia have been included from other workers for comparison. The Woorinen and Lowan samples are from Quaternary dunefields in the Murray Basin analyzed by Pell (1994), and the Kosciuszko sample is from an Ordovician turbidite in the Lachlan Orogen and was analyzed by Ireland et al. (1998). 3. ANALYTICAL BACKGROUND

3.1. Calculation of Statistical Adequacy Any provenance analysis is dependent on sampling statistics and probability. In the case of detrital geochronology a large quantity of data must be gathered to be reasonably certain that all significant protosource components contributing to the sediment have been sampled. Dodson et al. (1988) provide a test of statistical adequacy, being: P ⫽ (1 ⫺ f ) n

(1)

where P is the probability of missing a provenance component; f is the proportion of that component among the total provenance components; and n is the number of randomly selected grains analyzed. For example, at least 59 grains need to be measured to reduce the probability of missing a component comprising as little as 1 in 20 in the total provenance to 5% (Fig. 2).

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(Compston et al., 1984; Ireland, 1995). This in situ ability makes the SHRIMP an ideal platform for analyses requiring the relatively rapid acquisition of data from randomly selected grains. To enhance the quantity of measurements required for statistical adequacy, it is possible to reduce the amount of time spent counting isotopic species. Although this results in a reduction of precision, measurements remain sufficiently precise2 for provenance correlation in this study where a wide range of protosource ages is seen. Other studies with a narrower range of potential protolith ages may require greater precision and hence slower data acquisition. Detrital zircon grains were separated using standard crushing, milling, heavy liquid, and electromagnetic techniques and mounted in epoxy and polished to reveal half-sections. A number of steps are taken to ensure randomness and unbiased representation in zircon selection. The only grain size subdivision is a coarse screening of the milled sample at 250 ␮m (60-mesh), which does not affect the vast majority of detrital zircons. Also, unlike typical thermal ionization mass spectrometry work, there is no fine subdivision based on magnetic susceptibility, with simply the nonmagnetic fraction (typically at 2 A, 5° tilt) being used. A simple proportion of the nonmagnetic fraction is taken and only hand-picked to ensure mineral purity. No preferential selection of zircon is made on the basis of size, color, shape, or roundness during hand-picking. During analysis, operator bias in the analytical process is minimized by systematically working through a line of mounted zircon grains. The only operator choice is the avoidance of obvious imperfections in the grain surfaces. Zircon internal structures were interpreted from cathodoluminescence imaging and complex grains were analyzed when required in the systematic process. Using standard SHRIMP analytical techniques (e.g., Claoue´Long et al., 1995), Pb/Pb ratios were measured directly and Pb/U ratios by comparison with a known standard (SL13, 206 Pb/238U: 0.0928) analyzed sequentially with the unknown samples. Grain ages were calculated using either 206Pb/238U or 207 Pb/206Pb ratios depending on the age of the grain. Archean and early–middle Proterozoic grains with larger amounts of radiogenic Pb are more reliably assessed by their 207Pb/206Pb age corrected for common Pb by 204Pb measurements. As the amount of radiogenic Pb decreases with younger grain ages 206 Pb/238U ages become more precise. Even better precision using 207Pb measurements for correction of common Pb is possible for younger grains, although this approach is based on an assumption of concordance and a measurable mixture of common and radiogenic Pb. 4. DATA DISPLAY

3.2. SHRIMP Microanalysis

Uranium–lead geochronological measurements are typically displayed on Wetherill or Tera-Wasserburg concordia diagrams (Wetherill, 1956, 1963; Tera and Wasserburg, 1972, 1974). The primary usefulness of these diagrams is to identify measurements that are discordant and hence, considered less geologically informative. However, these diagrams lose clarity as the number of analyses increases and are difficult to assess visually

The SHRIMP ion probe is a secondary ion mass spectrometer from which ages of single mineral grains can be determined by the in situ measurement of uranium and lead isotopes

2 Precision is typically ⫾15–30 Ma at 2␴, depending on U content and common Pb correction.

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Fig. 2. Illustration of the P ⫽ (1 ⫺ f)n function with different proportions of components within the total population. For instance to reach 95% probability that a component has not been missed (i.e., 5% probability that it has been missed) when that component comprises 1 part in 20 of the total population, requires the measurement of 59 randomly selected samples.

for component subpopulations in detrital samples (e.g., Fig. 3). Alternatively, simple binned histograms have been used to display measured ages (e.g., Morton et al., 1996), but this approach results in the loss of visual information about measurement precision. There is also the problem of selecting an appropriate number and size of bins, again presenting the possibility of bias. For example, in the age frequency histograms of Figure 3, a small change in bin size from 25 to 20 Ma makes a subtle but distinct difference in the prominence of apparent modes in the distribution. The sets of age data in this article are displayed as probability density diagrams that are compiled by summing the gaussian distribution of each individual measurement, which is defined by the age and its error (Figs. 4 to 8). This approach follows the variable gaussian kernel probability density plots discussed by Silverman (1986):

f共t兲 ⫽

1 n

冘 n

i⫽1

1

␴ i 冑2 ␲

⫺共t⫺␮i兲2

e

2␴i2

(2)

where, in the case of geochronological measurements, ␮i is the ith age measurement and ␴i is the ith age measurement error and t is the age value for which the function is being calculated. To represent a true probability density distribution, the area under a curve is standardized to 1 by dividing by the number of individual measurements. For the sake of meaningful comparison such diagrams should also display the scale of the probability axis, the number of individual measurements visible in the age range shown, and the number of measurements outside the range. A probability density diagram can be a useful visual guide to component subpopulations and therefore, aid in comparison with other samples (e.g., Ireland et al., 1998). However, two factors may impede this usefulness. First, component populations may overlap and cannot be readily resolved in a probability density diagram. In such cases, further deconvolution may be achieved with mixture modeling (Sambridge and Compston, 1994). Second, as the number of analyzed samples increases simple visual comparison becomes increasingly awkward and possibly vulnerable to interpretation bias. At this

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Fig. 3. Illustration of orthodox techniques for displaying detrital zircon geochronological data using analyses from North Stradbroke Island. (a) Tera-Wasserburg diagram with analyses plotted uncorrected for common Pb. (b) Frequency histogram of ages based on 25-Ma wide bins. (c) Frequency histogram based on 20-Ma wide bins. Compare histograms with probability density distribution of Fig. 4b.

stage of data interpretation, further mathematical procedures are required as discussed below. 5. MULTIVARIATE ANALYSIS: METHOD, RESULTS, AND DISCUSSION

5.1. Data Treatment The problem faced when objectively describing, comparing, and interpreting a large set of geochronological data is similar to the problem found in the assessment of modal heavy mineral analyses, and a similar solution is proposed here. Traditional heavy mineral analysis of sand and sandstone samples involves the identification and counting of mineral species. Typically, 200 or more grains are counted, and percent abundance calculated (e.g., 12% tourmaline, 10% zircon). It is proposed here that a sample can be similarly defined in terms of frequency of detrital mineral ages. Zircon age data from the Australian samples were divided into 25 Ma divisions from 0 to 1200 Ma, with an extra division grouping together all ages older than 1200 Ma, making a total of 49 variables. Each data set was normalized to 100%, so that the resultant data are in the form of: 0 –24 Ma: 2.2%; 25– 49 Ma: 3.2%; 50 –74 Ma: 1.5%; etc. These data are given in Table 1. The decision to use 25-Ma divisions is arbitrary, and developing a method to ascertain the “ideal” division regime is an obvious area for further development. However, in this case, experimentation with 50 Ma, 100

Ma, and geological period divisions did not yield any increased benefit, and indeed obscured some of the details seen with the 25 Ma age divisions, such as the subdivision of lower order components by higher order components. The upper limit of 1200 Ma approximates the 90% percentile of the entire set of data. A number of assumptions have been made in the application of multivariate data analysis in this study and it is recognized that the described mathematical procedures and results require further refinement. The first assumption is that such age data, typically in the form of age ⫾ error, can be handled in a similar fashion to other data such as number percent mineral species. Yet, this assumption must be made because to treat each analysis as a discrete and “exact” age measurement is to ignore an important feature of geochronological analysis—namely that any age measurement is always associated with an analytical error. To do otherwise is to weight all measurements equally. For example, an age of 510 ⫾ 40 Ma would be treated the same as 510 ⫾ 1 Ma when it is obvious that the first age is less precise and in reality could span a greater range of ages and overlap more than one age division. To accommodate the age measurement errors, the samples have not been simply binned into 25 Ma divisions according to age measurements alone. Rather, the probability density function discussed previously has been used to calculate the percentage of the age distribution in each division. For instance, using simple binning, the per-

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Fig. 4. Probability distribution diagrams of the zircon ages for eastern coastal samples. Number of zircon ages represented by each curve is given, plus the number of ages (in brackets) ⬎1200 Ma in the sample. Area under each curve is normalized to one with probability as the vertical scale (scales may differ between samples for clarity).

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Fig. 4. Continued.

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Fig. 5. Probability distribution diagrams of the zircon ages for Murray Basin samples. Number of zircon ages represented by each curve is given, plus the number of ages (in brackets) ⬎1200 Ma in the sample. Area under each curve is normalized to one with probability as the vertical scale (scales may differ between samples for clarity). *Lowan and Woorinen data from Pell (1995).

centage values for ages measured at Hummock Hill Island in the 25 Ma age divisions between 125 and 249 Ma would be: 125–149 Ma: 0.00%; 150 –174 Ma: 1.33%; 175–199 Ma: 0.00%; 200 –224 Ma: 5.33%; and 225–249 Ma: 22.67%. Using

the probability density function to account for the errors in the measured ages yields 125–149 Ma: 0.01%; 150 –174 Ma: 1.00%; 175–199 Ma: 0.46%; 200 –224 Ma: 7.28%; and 225– 249 Ma: 18.33%. Experimentation with both methods for de-

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Fig. 5. Continued.

scribing the distribution was done. Although there is distinct difference between values for the derived components and sample scores, the significant relationships and trends among the samples, as discussed later, for the probability distributions remained essentially similar. Two further assumptions are related to normalizing the divisions to a proportion of the total. The use of such proportions can introduce spurious negative correlations because of closure (Chayes, 1960). If one variable is relatively large, then by definition other variables are limited to being smaller because they must sum to 100%. It has been shown that principal components derived from such a closed array are also by definition a closed array with the possibility of imposed correlation (Chayes and Trochimczyk, 1978). Although the effects of closure generally decrease with an increasing number of variables, a large number of variables are not an automatic guarantee that closure bias will be absent (Kucera and Malmgren, 1998). The effects of closure can be eliminated

using a log–ratio transformation of the data described in the Appendix (Aitchison, 1986). The third assumption is that with normalization every sample is treated with equal importance. This may result in bias itself if a group of samples are very similar, or if a single sample is very dissimilar. An attempt has been made in this study to collect and analyze samples across a wide range of geography and stratigraphy to prevent any one potential protosource being too heavily represented (e.g., the eastern coastal samples are at roughly regular intervals along the coast). However, the sampling program is in a sense informal and has not used experimental design procedures that would introduce a random element to help avoid sample bias. Given the complexity inherent in any geological investigation any such random sampling program may be very difficult to implement. The data analyses described were originally obtained using the Genstat 5 Release 3.2 statistical analysis package (Payne et al., 1993) running on a Sun Microsystems SPARCsystem 600

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Fig. 6. Probability distribution diagrams of the zircon ages for Sydney Basin samples. Number of zircon ages represented by each curve is given, plus the number of ages (in brackets) ⬎1200 Ma in the sample. Area under each curve is normalized to one with probability as the vertical scale (scales may differ between samples for clarity).

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Fig. 7. Probability distribution diagrams of the zircon ages for southeastern Australian fluvial samples. Number of zircon ages represented by each curve is given, plus the number of ages (in brackets) ⬎1200 Ma in the sample. Area under each curve is normalized to one with probability as the vertical scale (scales may differ between samples for clarity). †Kosciuszko data from Ireland et al. (1998).

(Sircombe, 1997), although the procedures have subsequently been implemented as Microsoft Excel macros.3 Many of the algorithms described are also implemented in a variety of statistical or multivariate analysis packages available for desktop computers. 5.2. Principal Component Analysis Principal component analysis (PCA) is a mathematical method for assessing variable groupings within multivariate data. It has been used widely in previous provenance studies using heavy mineral analysis (e.g., Pirkle et al., 1984, 1985;

3 Macros are available upon request from author or the Continental Geoscience Division, Geological Survey of Canada.

Clemens and Komar, 1988; Wagreich and Marschalko, 1995). The method takes p variables (X1, X2, X3, . . . , Xp) and finds indices Z1, Z2, Z3, . . . , Zp that are uncorrelated and explain a decreasing proportion of the total variability in the data. These uncorrelated indices are in effect “dimensions” within the data that explain the data in fewer variables than the original number. An analogy of this process is how a three-dimensional object can be simplified, but still portrayed meaningfully, as a two-dimensional drawing. In the cases discussed here, the “object” is a multidimensional construct that is being simplified to fewer more manageable, but still meaningful, dimensions. The distinct difference between principal component analysis and factor analysis should be made clear. The term factor analysis is often used in a generic sense to describe all procedures that assess multivariate data for underlying structure or

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Fig. 7. Continued.

“factors.” However, PCA yields “components” that are combinations of the original variables, whereas “true” factor analysis yields factors that are combined with a unique constant to express the original variables. Another important difference between PCA and factor analysis is in the use of previous assumptions about the nature of the data. PCA is essentially a mathematical procedure where no attention is given to probability or significance testing. In comparison, factor analysis is a statistical procedure and heavily based on previous assumptions about the number of factors actually present in the data (Davis, 1986, p. 546). To avoid these assumptions, PCA has been chosen to provide an objective assessment of the geochronological data discussed here. A description is given in the Appendix, but is only intended as a brief synopsis of the procedure. The reader is referred to texts such as Davis (1986), Manly (1994), and Wackernagel (1995) for more details of the methods involved. When applied to the zircon age data with 49 variables (age

divisions) PCA produced 30 non-zero principal components listed in Table 2. The first 13 of these principal components account for ⬎95% of the total variance in the data, although for the purposes of concise discussion, only the first three principal components will be examined in detail. The loading by each variable, or age division, on the first three principal components are given in Table 3 and illustrated with bar diagrams to aid interpretation in Figure 9. The scores of each component for the 31 samples are given in Table 4 and are illustrated in Figures 10 to 12. From Figure 9a, Component I is interpreted as a measure of the amount of 75– 475 Ma ages vs. ⬎475 Ma ages. A positive Component I score indicates a relatively larger presence of ages ⬎475 Ma as seen in the West Australian Augusta and Minninup samples (Figs. 8c, 8d and 10, upper right), which are almost entirely comprised of these ages. Conversely, a negative Component I score indicates the relatively larger presence of 75– 475 Ma ages, as clearly seen in the Terrigal sample (Figs.

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Fig. 8. Probability distribution diagrams of the zircon ages for Western Australian samples. Number of zircon ages represented by each curve is given, plus the number of ages (in brackets) ⬎1200 Ma in the sample. Area under each curve is normalized to one with probability as the vertical scale (scales may differ between samples for clarity).

6c and 10, center left), which is dominated (83.1%) by 75– 475 Ma ages. Component II illustrates how PCA works by grouping together otherwise disparate age groups under one component. A positive Component II score indicates the greater presence of

ages in either a 75–275 Ma or 575– 875 Ma age range, for example, the Hispanola sample (Figs. 5b and 10, upper left), which has a total of 51.3% of ages within these two age ranges. A negative Component II score (Fig. 9b) indicates a relatively larger presence of 275–575 Ma ages with a minor contribution

WIM150

Robinvale

Hispanola

Spring Hill

Lorne

Mallacoota

Boydtown

Aslings #2

Aslings #1

Shoalhaven Hds.

Tomago

Stockton

Coffs Hbr.

N. Stradbroke Is.

Hummock Hill Is. MB H 82 0.00 0.00 0.00 0.00 0.79 2.51 3.69 2.77 0.00 1.74 1.82 1.63 2.58 2.81 1.39 1.83 5.52 6.09 3.61 4.88 5.95 5.30 4.46 3.59 2.38 1.83 1.53 2.30 1.71 0.51 0.31 0.50 0.29 0.06 0.01 0.03

Woorinen*

MB PP 61 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.32 1.24 2.15 10.19 14.63 13.55 9.75 8.45 5.39 2.16 3.22 3.77 1.85 0.42 0.31 0.92 1.12 0.69 0.52 0.59 0.68 0.70 0.60 0.54 0.71 0.85

MB H 77 0.00 0.00 0.00 0.55 4.63 2.67 1.24 1.71 2.27 4.02 1.08 1.32 3.86 1.47 1.60 3.33 2.39 1.39 1.15 1.48 1.25 5.05 4.13 3.37 5.26 4.88 2.63 0.99 0.36 0.59 1.38 0.19 0.00 0.03 0.85 0.99

Lowan*

MB PP 74 1.35 0.00 0.00 0.00 0.00 0.87 4.05 3.99 0.57 1.28 3.49 0.73 0.73 0.47 0.04 0.42 1.13 0.75 0.45 0.90 4.32 9.26 14.79 16.95 11.52 5.58 2.82 1.36 0.67 0.41 0.26 0.16 0.13 0.14 0.16 0.17

SB PM 53 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 1.56 8.25 7.20 4.86 10.79 24.70 9.11 2.61 2.79 2.87 2.49 2.53 3.61 1.36 0.14 0.00 0.00 0.00 0.05 0.30 0.95 1.27 0.80 0.32 0.16

Tallong

MB PP 65 0.00 0.00 0.00 0.03 9.73 4.31 5.62 1.16 2.12 8.03 4.36 2.98 2.86 4.41 0.54 0.58 0.96 1.59 2.38 0.78 0.97 1.68 2.75 4.96 2.57 0.75 0.69 1.59 0.78 0.45 1.25 1.15 0.49 0.66 0.53 0.12

SB TR 77 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.50 10.17 7.53 5.01 23.22 16.75 7.55 5.13 5.24 1.82 0.19 0.11 0.86 0.89 1.41 1.88 1.11 0.22 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Terrigal

MB PP 65 0.00 1.54 0.00 0.03 3.53 4.25 7.56 2.70 2.46 3.86 4.48 1.88 0.00 0.57 1.92 1.23 2.37 0.60 1.08 2.18 6.56 8.46 7.91 3.69 2.72 1.08 0.13 0.09 0.10 0.10 0.17 0.90 2.04 1.50 0.42 0.11

SB TR 87 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.03 0.89 1.49 0.15 0.10 0.09 0.09 0.44 2.23 1.64 0.59 1.97 5.74 8.65 10.57 10.49 9.48 6.13 3.78 2.11 1.16 0.61 0.42 0.51 0.76 0.95 0.89 0.64

Hawkesbury (Calga)

MB H 68 0.00 0.00 0.00 2.26 17.38 0.94 0.00 0.00 0.02 2.32 3.47 0.23 0.83 1.34 1.71 4.31 3.58 3.19 4.35 8.02 6.08 4.13 6.05 7.19 4.47 1.63 0.30 0.02 0.00 0.00 0.01 0.11 0.36 0.54 0.34 0.10

SB TR 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 1.64 0.81 0.55 0.58 0.71 1.51 0.16 0.00 0.02 0.16 2.20 3.90 6.63 11.13 8.44 7.47 3.99 1.86 1.41 1.17 0.64 0.94 1.93 1.85 1.20 1.36 1.88

Hawkes. (Bundeena)

EA H 87 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 2.00 0.32 0.98 3.13 13.52 20.73 2.29 1.43 6.74 5.18 9.01 9.14 2.25 1.94 3.75 1.37 0.08 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

SEA OR 100 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.18 1.27 4.28 7.06 3.91 5.38 3.92 3.97 3.90 2.90 1.41 0.91 0.78 0.10 0.00 0.00 0.01 0.08 0.35

Kosciuszko†

EA H 64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.86 0.70 0.46 7.88 29.39 29.81 5.60 1.73 2.10 1.11 0.88 1.72 1.34 1.05 0.75 0.52 0.62 0.74 0.21 0.01 0.00 0.00 0.00 0.01 0.09

SEA CB 60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 1.18 3.89 11.34 10.94 3.96 1.89 1.99 4.15 5.41 7.10 5.79 3.11 1.22 0.99 1.47 1.24 0.37 0.04 0.00 0.00 0.03 0.18 0.64 1.51 2.36

Bombala

EA H 60 0.00 0.00 0.00 0.01 0.00 1.69 0.00 0.07 1.20 0.42 0.02 0.26 1.15 2.51 5.18 10.43 12.92 8.22 4.96 5.51 5.54 5.19 5.33 4.94 3.36 1.63 0.78 0.68 0.84 0.92 0.79 0.50 0.27 0.18 0.16 0.17

SEA DV 65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.45 3.42 7.23 13.18 8.01 3.66 4.57 6.22 7.09 7.32 6.21 4.17 3.01 2.37 1.82 1.61 1.35 0.97 0.65 0.48 0.51 0.69 0.86

Kilbrechin

EA H 73 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.63 0.67 0.94 1.97 0.64 3.42 10.60 13.38 8.06 8.65 8.53 4.42 4.20 5.04 3.47 2.72 1.36 0.59 0.54 0.71 0.70 0.44 0.16 0.04 0.03 0.11 0.28

SEA T 51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.22 0.85 2.05 11.34 24.04 14.32 6.50 4.81 3.88 4.18 3.37 2.59 1.19 1.16 1.49 1.30 0.83 0.36 0.09 0.01 0.00 0.02 0.56 1.15

Tuross Head

EA H 43 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 1.09 2.97 0.74 1.72 0.45 0.82 5.83 9.90 4.77 3.76 7.07 7.75 7.71 8.21 6.64 3.86 2.01 1.50 1.16 0.69 0.29 0.07 0.01 0.01 0.05 0.22 0.56

SEA T 40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.49 2.83 4.96 3.53 0.36 0.62 6.79 12.38 10.24 4.83 4.09 3.78 2.11 3.66 3.33 2.26 2.51 2.35 1.63 1.10 1.22 1.39 1.14 1.07 1.05 0.56 0.13

Brooman

EA PP 57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.61 1.14 0.00 0.00 0.12 1.22 0.41 0.00 0.00 0.08 1.00 5.93 15.40 17.59 16.45 13.10 4.66 3.25 1.44 0.45 0.43 0.43 0.29 0.15 0.26 0.89 1.13

SEA H 81 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.28 3.21 6.37 18.13 25.52 10.70 4.22 4.17 2.95 2.41 2.01 1.30 1.41 1.55 1.16 0.75 0.58 0.91 0.87 0.34 0.14 0.31 0.53

Halfway Flat

EA H 77 0.00 0.00 0.00 0.80 1.76 0.00 0.00 0.00 0.00 0.00 0.06 0.56 1.10 2.17 2.65 2.53 1.97 1.29 0.68 1.17 3.36 6.87 10.26 11.59 9.73 6.88 5.77 4.67 2.78 1.25 0.53 0.25 0.24 0.44 0.76 0.96

WA H 88 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.11 0.49 0.88 1.90 9.16 18.83 21.13 14.44 6.51 3.54 1.69 0.59 0.21 0.10 0.33 0.51 0.22 0.06 0.17 0.44 0.63

Eneabba

EA H 84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.21 1.90 3.14 0.75 1.24 5.28 6.27 4.08 2.74 2.28 1.67 2.57 5.57 8.67 10.81 10.00 8.12 4.80 2.15 1.01 0.50 0.34 0.26 0.26 0.43 0.61 0.65 0.67

WA H 59 0.00 0.00 0.00 0.00 0.60 1.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.05 1.02 2.83 4.38 2.20 2.31 2.67 3.74 6.13 7.56 5.16 2.04 0.81 0.73 0.92 1.15 1.25 1.07

Minninup

EA H 91 0.00 0.00 0.00 0.01 0.02 0.05 0.09 0.30 2.28 4.43 2.46 1.63 2.69 3.90 3.06 3.04 3.07 2.42 3.28 4.19 5.10 5.96 6.08 5.63 4.27 3.24 2.54 1.77 1.42 1.48 1.51 1.26 0.97 0.82 0.82 0.97

WA WA H H 56 63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.04 0.00 0.20 0.00 0.48 0.00 0.52 0.00 0.27 0.03 0.12 0.59 0.74 2.06 1.02 2.96 1.89 3.20 1.13 2.87 1.99 4.03 2.57 7.34 3.99 12.08 6.29 16.13 7.45 16.25 5.56 11.23 2.86 5.40 1.35 2.13 0.64 0.76 0.60 0.28 0.80 0.15 0.94 0.15 0.93 (Continued)

Augusta

EA H 75 0.00 0.00 0.00 0.00 0.00 0.01 1.00 0.46 7.28 18.33 8.39 2.70 3.96 4.53 3.30 0.70 0.02 0.13 0.88 2.07 4.97 8.17 6.33 5.56 3.04 3.29 1.92 0.82 0.15 0.01 0.02 0.12 0.36 0.92 0.95 0.25

Waroona

Region Age of dep. #analyses 0–24 Ma 25–49 Ma 50–74 Ma 75–99 Ma 100–124 Ma 125–149 Ma 150–174 Ma 175–199 Ma 200–224 Ma 225–249 Ma 250–274 Ma 275–299 Ma 300–324 Ma 325–349 Ma 350–374 Ma 375–399 Ma 400–424 Ma 425–449 Ma 450–474 Ma 475–499 Ma 500–524 Ma 525–549 Ma 550–574 Ma 575–599 Ma 600–624 Ma 625–649 Ma 650–674 Ma 675–699 Ma 700–724 Ma 725–749 Ma 750–774 Ma 775–799 Ma 800–824 Ma 825–849 Ma 850–874 Ma 875–899 Ma

Location

Table 1. Table of age division percentage data for the zircon samples analyzed.

1606 K. N. Sircombe

Terrigal

Tallong

Lowan*

Woorinen*

WIM150

Robinvale

Hispanola

Spring Hill

Lorne

Mallacoota

Boydtown

Aslings #2

Aslings #1

Shoalhaven Hds.

Tomago

Stockton

Coffs Hbr.

N. Stradbroke Is.

Hummock Hill Is. 0.80 0.54 0.35 0.58 0.93 0.85 0.57 0.23 0.13 0.34 0.56 0.40 7.83

0.19 0.00 0.02 0.07 0.24 0.55 0.94 1.20 1.15 0.84 0.47 0.20 7.78

0.01 0.00 0.00 0.00 0.03 0.17 0.58 1.20 1.70 1.92 2.02 2.02 9.79

0.59 0.57 1.16 0.55 0.33 1.68 0.51 0.14 2.14 0.79 0.13 2.12 1.24 0.28 2.01 1.19 0.48 1.99 0.79 0.62 2.02 0.61 0.64 1.88 0.60 0.63 1.72 0.53 0.74 3.50 0.37 1.18 4.55 0.24 0.98 4.26 2.16 11.30 23.12

0.20 1.04 0.26 1.30 0.30 1.53 0.29 1.95 0.27 2.23 0.31 1.90 0.52 1.47 0.88 1.96 1.13 3.75 1.08 5.52 0.83 5.37 0.53 3.93 5.74 25.51

Region abbreviations: EA, Eastern Australia; MB, Murray Basin; SB, Sydney Basin; SEA, Southeastern Australia; WA, Western Australia. Age of deposition abbreviations: H, Holocene; PP, PlioPliestocene; T, Tertiary; TR, Triassic; PM, Permian; CB, Carboniferous; DV, Devonian; OR, Ordovician. † Sample data provided by T. R. Ireland (Ireland et al., 1998). * Sample data from S. Pell (Pell et al., 1997).

0.00 0.46 0.89 0.72 2.44 0.01 0.49 0.51 1.15 2.03 0.08 0.63 1.20 1.47 2.10 0.29 0.86 2.16 1.60 2.20 0.78 1.29 2.72 1.61 1.90 1.34 1.87 2.09 2.66 1.56 1.42 1.96 0.98 3.71 1.15 0.88 1.57 1.45 3.83 0.71 0.31 1.23 1.90 3.32 0.54 0.07 0.95 1.51 2.10 0.60 0.01 0.69 1.05 1.83 0.55 0.00 0.49 0.37 2.07 0.31 5.20 14.60 19.03 33.42 13.04

Hawkesbury (Calga)

0.29 0.56 0.78 0.87 0.89 0.92 1.00 1.06 1.01 0.82 0.59 0.35 2.10

Hawkes. (Bundeena)

0.70 0.15 0.78 0.46 0.35 1.27 0.27 0.42 2.40 0.12 0.31 1.56 0.04 0.39 1.59 0.02 0.78 1.32 0.10 1.38 0.46 0.34 1.65 0.39 0.57 1.23 0.40 0.56 0.95 0.52 0.80 0.87 0.67 1.49 0.75 0.77 9.19 16.34 19.74

Kosciuszko†

0.16 0.15 0.14 0.14 0.17 0.22 0.25 0.25 0.21 0.15 0.08 0.04 8.13

Bombala

0.05 0.23 0.03 0.19 0.55 0.24 0.51 0.87 1.22 0.80 1.02 1.97 0.80 0.65 1.80 0.64 0.76 1.56 0.67 0.95 1.41 0.88 0.67 1.17 1.05 0.76 0.74 0.95 1.15 0.47 0.56 1.14 0.42 0.20 0.56 0.43 7.40 12.45 14.70

Kilbrechin

0.07 0.63 1.59 1.22 0.72 0.58 0.67 0.42 0.66 1.10 1.02 0.48 6.94

Tuross Head

0.34 0.57 0.50 0.49 0.71 0.85 0.83 0.69 0.54 0.37 0.18 0.06 6.26

Brooman

0.19 0.25 0.34 0.41 0.42 0.34 0.25 0.21 0.29 0.53 0.79 0.76 9.37

Halfway Flat

0.50 0.64 0.70 0.91 1.30 1.26 0.75 0.46 0.42 0.39 0.30 0.17 9.83

Eneabba

0.79 0.84 0.37 0.83 0.09 0.67 0.07 0.57 0.29 0.49 0.65 0.44 0.86 0.51 0.81 0.65 0.56 0.74 0.32 0.75 0.41 0.74 0.62 0.75 7.68 12.07

Minninup

0.97 0.95 1.11 1.46 1.75 1.76 1.49 1.08 0.67 0.34 0.14 0.04 5.14

Augusta

0.03 1.03 0.58 0.00 0.87 0.36 0.00 0.67 0.17 0.00 0.58 0.10 0.00 0.58 0.13 0.01 0.63 0.17 0.05 0.70 0.21 0.19 0.73 0.20 0.38 0.64 0.16 0.41 0.47 0.11 0.24 0.31 0.06 0.10 0.20 0.03 7.96 11.77 10.73

Waroona

900–924 Ma 925–949 Ma 950–974 Ma 975–999 Ma 1000–1024 Ma 1025–1049 Ma 1050–1074 Ma 1075–1099 Ma 1100–1124 Ma 1125–1149 Ma 1150–1174 Ma 1175–1199 Ma ⬎1200 Ma

Location

Table 1. (Continued)

Quantitative comparison 1607

1608

K. N. Sircombe

Table 2. Eigenvalues and percentage total variation for the 27 nonzero principal components derived from the zircon age data. Principal component #

Eigenvalue

% Variance

Cumulative variance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

67.82 43.53 23.10 14.41 13.66 9.10 7.58 6.51 5.56 4.09 3.58 3.24 2.69 2.12 2.04 1.50 1.19 0.70 0.55 0.46 0.40 0.30 0.25 0.21 0.17 0.12 0.09 0.07 0.03 0.02

31.53 20.24 10.74 6.70 6.35 4.23 3.52 3.03 2.58 1.90 1.66 1.51 1.25 0.99 0.95 0.70 0.56 0.32 0.26 0.21 0.19 0.14 0.12 0.10 0.08 0.06 0.04 0.03 0.01 0.01

31.53 51.77 62.51 69.21 75.56 79.79 83.32 86.34 88.93 90.83 92.49 94.00 95.25 96.24 97.18 97.88 98.44 98.76 99.02 99.23 99.42 99.56 99.67 99.77 99.85 99.91 99.95 99.98 99.99 100.00

Total

215.09

100.00

of ages ⬎875 Ma. This is most prominent at Mallacoota (Figs. 4j and 10, bottom center) with 90.8% of the ages within these ranges. Mallacoota also has a strongly positive Component III score, which indicates the presence of 75–200 Ma or 400 – 450 Ma ages (Figs. 4j and 11, top center). In the case of Mallacoota, this component is a measure of the latter range because it has no ages within the former range. In comparison, Lorne is another sample with a high positive Component III score with 20.6% in the 75–200 Ma age range (Figs. 5e and 11, upper left). A strongly negative Component III score is illustrated by Hummock Hill Island indicating the presence of 200 – 400 Ma (49.2%) and 450 –925 Ma ages (39.9%) (Figs. 4a and 11, lower left). 5.3. Geological Interpretation of Principal Components To aid the provenance analysis of the detrital zircon, the derived principal components are interpreted in terms of a priori knowledge of Australian geological history as outlined above. In this case it is fortunate that the principal components can be assigned a geological meaning relatively easily. Nevertheless, it should be stressed that the principal components, which describe the samples, are derived from the samples themselves, rather than imposed from expected patterns based on knowledge of the geology. Component I is interpreted as a measure of “local” vs.

Table 3. Eigenvectors or variable loadings on the first five principal components. Principal components Age divisions

I

II

III

0–24 25–49 50–74 75–99 100–124 125–149 150–174 175–199 200–224 225–249 250–274 275–299 300–324 325–349 350–374 375–399 400–424 425–449 450–474 475–499 500–524 525–549 550–574 575–599 600–624 625–649 650–674 675–699 700–724 725–749 750–774 775–799 800–824 825–849 850–874 875–899 900–924 925–949 950–974 975–999 1000–1024 1025–1049 1050–1074 1075–1099 1100–1124 1125–1149 1150–1174 1175–1199 1200–

0.0291 0.0280 0.0493 ⫺0.0405 ⫺0.0638 ⫺0.0818 ⫺0.1340 ⫺0.1340 ⫺0.2233 ⫺0.2884 ⫺0.2873 ⫺0.3124 ⫺0.3135 ⫺0.2525 ⫺0.1937 ⫺0.1935 ⫺0.1906 ⫺0.1515 ⫺0.0529 0.0284 0.0380 0.0397 0.0253 0.0243 0.0421 0.0766 0.1416 0.1771 0.2018 0.2042 0.1512 0.0895 0.0812 0.0761 0.1038 0.1336 0.1427 0.1202 0.0890 0.0844 0.0841 0.0729 0.0629 0.0626 0.0689 0.0883 0.1141 0.1393 0.0434

⫺0.0196 ⫺0.0015 ⫺0.0691 0.0439 0.2192 0.3063 0.3053 0.2865 0.2326 0.3106 0.1918 ⫺0.0431 ⫺0.1454 ⫺0.1430 ⫺0.2303 ⫺0.2773 ⫺0.3316 ⫺0.2761 ⫺0.1574 ⫺0.1009 ⫺0.0526 ⫺0.0217 ⫺0.0180 0.0055 0.0184 0.0089 0.0346 0.0604 0.0751 0.0515 0.0877 0.1099 0.0913 0.0860 0.0304 ⫺0.0263 ⫺0.0793 ⫺0.0636 ⫺0.0665 ⫺0.0760 ⫺0.0834 ⫺0.0639 ⫺0.0547 ⫺0.0395 ⫺0.0364 ⫺0.0347 ⫺0.0260 ⫺0.0114 ⫺0.0065

⫺0.0539 0.0498 ⫺0.0236 0.2320 0.4470 0.3136 0.0834 0.0932 ⫺0.0663 ⫺0.1508 ⫺0.1932 ⫺0.0476 ⫺0.1246 ⫺0.0774 ⫺0.0846 ⫺0.0513 0.1077 0.0386 ⫺0.0078 ⫺0.0119 ⫺0.0372 ⫺0.0384 ⫺0.0407 ⫺0.0411 ⫺0.0306 ⫺0.0526 ⫺0.1017 ⫺0.1365 ⫺0.1804 ⫺0.1391 ⫺0.1335 ⫺0.1589 ⫺0.2020 ⫺0.1764 ⫺0.1580 ⫺0.1345 ⫺0.0072 0.2013 0.2645 0.2769 0.2140 0.1529 0.0879 0.0319 0.0115 0.0210 0.0221 0.0116 0.0008

“exotic” provenances particularly in southeastern Australia. The 75– 475 Ma ages form a negative Component I value, which are typical of the Phanerozoic orogens of eastern Australia. Potential protosources in this age range include the Silurian–Devonian granites and Ordovician turbidites of the Lachlan Orogen (Compston and Chappell, 1979; Williams et al., 1983; Williams, 1992; Turner et al., 1993, 1996); the Carboniferous through to Triassic granites and volcanics of the New England Orogen (Green, 1973; Flood and Shaw, 1977; Shaw and Flood, 1981; Coney et al., 1990); and the Jurassic and Cretaceous volcanic arc activity along the Queensland margin (e.g., Whitsunday Volcanic Province; Ewart et al.,

Quantitative comparison

1609

Fig. 9. Graphic representation of the loadings of each variable (age division) on the first three principal components derived from the zircon age data.

1992) and possibly along the entire length of the present coast to the Otway/Gippsland Basins in the south (Bryan et al., 1997). Conversely, the positive loadings of the 475-Ma and older age range in Component I, particularly those ⬎550 Ma, are considered exotic to eastern Australia with an enigmatic protosource location, but possibly in modern East Antarctica (Sircombe, 1999). This age component has previously been termed the Neoproterozoic Pacific-Gondwana component and is a common feature of detrital geochronology elsewhere in the region (e.g., Williams et al., 1991, 1994; Ireland et al., 1994,

1998; Wysoczanski et al., 1997). In Western Australia this age range also includes the prominent presence of Mesoproterozoic ages, which given the seeming dominance of Archean geology in that region may also be considered exotic to that region (Sircombe and Freeman, 1999). Indeed the four West Australian samples along with the Kosciuszko sample have the largest positive Component I scores, indicating that their inclusion in this set of age data may be largely responsible for the nature of this component. A score around zero indicates a balanced mix between the two (e.g., Aslings #1 and Shoalhaven Heads). Component II is interpreted as a subdivision of the local and

1610

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Table 4. Principal component scores of the 31 zircon samples for the first three principal components. Principal components Samples

I

II

III

Hummock Hills Is. N. Stradbroke Is. Coffs Hbr. Stockton Beach Tomago Sands Shoalhaven Hds. Aslings #1 Aslings #2 Boydtown Mallacoota Spring Hill Hispanola Robinvale WIM150 Lorne Hawkesbury Calga Hawkes. Bundeena Terrigal Tallong Woorinen Lowan Kosciuszko Brooman Tuross Head Kilbrechin Halfway Flat Bombala Eneabba Minninup Augusta Waroona

⫺7.92 ⫺1.93 ⫺1.41 5.90 10.45 0.15 ⫺0.13 ⫺0.97 1.44 ⫺1.90 ⫺2.20 ⫺4.51 ⫺2.05 1.94 ⫺5.10 7.20 4.10 ⫺14.48 ⫺1.11 ⫺2.67 ⫺3.68 16.37 ⫺1.05 4.37 10.28 9.78 1.66 13.23 20.22 19.74 16.23

1.86 ⫺3.05 ⫺8.94 ⫺11.22 ⫺2.72 ⫺11.60 ⫺12.49 ⫺6.81 ⫺17.52 ⫺17.30 3.36 3.02 1.16 ⫺14.38 ⫺6.60 ⫺4.43 ⫺2.74 ⫺10.85 ⫺16.79 ⫺2.41 ⫺0.25 ⫺7.14 ⫺8.58 ⫺15.67 ⫺13.72 ⫺14.29 ⫺16.32 ⫺9.07 1.30 ⫺0.57 ⫺9.27

⫺14.26 ⫺5.79 ⫺10.53 ⫺1.14 ⫺8.44 ⫺5.96 ⫺5.85 ⫺0.87 0.19 3.25 2.67 0.88 ⫺6.08 ⫺8.70 3.98 ⫺8.99 ⫺3.21 ⫺1.11 ⫺2.23 ⫺0.03 3.32 1.52 ⫺13.99 ⫺4.90 ⫺4.92 ⫺3.16 ⫺2.42 ⫺2.87 1.48 ⫺6.00 ⫺3.62

exotic provenances seen in Component I. The 75–275 Ma age range of a positive Component II can be correlated with younger parts of the New England Orogen and the Whitsunday Volcanic Province as described above. This age range is most clearly expressed in the upper left quadrant of Figure 10 with samples from the northern coastline and most of the Murray Basin samples. The presence of Jurassic and Cretaceous ages in the Murray Basin probably reflects a provenance pathway through the volcaniclastic sediments of the Eromanga Basin that lies upstream of the Murray Basin (Fig. 1). These extensive volcaniclastic sediments were shed from the late Paleozoic Queensland volcanic provinces (Veevers, 1984) and have probably been subsequently recycled to contribute to the Cenozoic Murray Basin sediments. A positive Component II also includes the 600 –900 Ma age range, again most clearly illustrated in the Minninup sample from Western Australia. A negative Component II includes the 275–575 Ma age range, which covers older sections of the sections of the New England Orogen, the Lachlan Orogen, and minor contributions from the younger end of the Pacific–Gondwana provenance, which has been interpreted as being derived from the Ross– Delamerian Orogeny (Sircombe, 1999). This grouping reflects a reality that, although strongly demarcated by geological study, these three orogens actually overlap in time. The samples displaying the strongest negative Component II scores are those with strong geographic and fluvial links to sources in the

Lachlan Orogen (e.g., Mallacoota, Boydtown, Tallong, and Bombala). The sensitivity of the PCA can been seen with the duplicate samples from Aslings Beach. Sampled 18 months apart, the age distributions appear similar (Fig. 4g,h), although with PCA they are separated in Figure 10 by differing Component II scores—a result of one Cretaceous-aged grain in the resample. However, one solitary grain cannot be the basis to determine that a significant provenance change occurred within the 18 months between samples. Finally, Component III is interpreted as a complex mixture of provenances, probably typical of the melange that PCA will produce in higher order components representing a decreasing proportion of total variance. A positive Component III score is interpreted as the presence of Cretaceous–Jurassic Queensland volcaniclastics, a more tightly constrained Early Devonian– Silurian Lachlan Orogen and the Mesoproterozoic provenances. The Murray Basin samples again feature prominently with this Component, despite their distance from the original source region (Fig. 11, upper left). The similarity of the Lorne beach sample with the Murray Basin samples is why it has been grouped with the Murray Basin group (Fig. 5). With a provenance pathway through the Otway–Gippsland Basins rather than the Eromanga Basin as in the Murray Basin samples, the similar presence of Cretaceous and Jurassic ages provides tentative evidence for the Queensland volcanic province extending along the entire eastern coastline (Bryant et al., 1997). A negative Component III score indicates the presence of 200 – 400 Ma and 450 –925 Ma ages, which can be interpreted as a combination of the New England Orogen and Pacific– Gondwana provenances. This is most clearly seen at Hummock Hill Island, which is the furthest distance geographically and in terms of the south to north littoral drift system from the 400 – 475 Ma ages of the Lachlan Orogen provenance. 5.4. Modeling Provenance Pathways The strong south to north littoral drift system along a near continuous stretch of the eastern coastline (Roy and Thom, 1981) passes a variety of geological hinterlands. This setting provides a good case example to further demonstrate the usefulness of multivariate analysis for the geological interpretation of large sets of geochronological data. A visual examination of the 10 zircon age distributions in Figure 4 would suggest an evolution of dominant provenances along the coast between the northernmost sample at Hummock Hill Island and the southernmost sample at Mallacoota. Although the evolution can be seen (Fig. 12, inset), describing it would be difficult and PCA provides a means to quantify and illustrate this pattern in Figure 12 using the derived Components I and II. Samples from the southern end of the coastline tend to have larger negative Component II scores (except for the Aslings Beach resample for reasons discussed above). This indicates a Lachlan Orogen provenance that becomes diluted as the drift proceeds northward. This trend is broken in the central section of the coastline by the Stockton Beach and Tomago Sands samples with a positive Component I scores. This indicates the dominant presence of the Neoproterozoic Pacific–Gondwana provenance. PCA and Figure 12 is able to suggest a source for this sudden intrusion of the exotic provenance despite the

Quantitative comparison

1611

Fig. 10. Zircon samples plotted using scores of principal components I and II with indication of what ages those components represent.

absence of any suitable outcrop. The Stockton Beach and Tomago Sands samples can be considered similar to the two Hawkesbury Sandstone samples, which are also dominated by the Neoproterozoic Pacific–Gondwana provenance. It is interpreted that the Hawkesbury Sandstone is an intermediate repository for this provenance, although the ultimate location of the protosource is unclear (Sircombe, 1999). Continuing northward both the Lachlan Orogen and Pacific–Gondwana provenance are diluted by the New England Orogen provenance resulting in increasingly negative Component I and positive Component II scores.

5.5. Further Developments The work presented illustrates the value of using multivariate analysis in objectively assessing detrital geochronological data. The Australian example presented here works well because the geology of potential protosources is well enough known to allow interpretation of the principal components. Obviously, there will be geological situations where such a priori knowledge is limited or absent, and indeed the purpose of detrital geochronology is for reconnaissance. Further development of the methods presented could be useful in these situations.

1612

K. N. Sircombe

Fig. 11. Zircon samples plotted using scores of principal components I and III with indication of what ages those components represent.

Factor analysis algorithms for heavy mineral analysis have been developed to find end-members within the data assuming that the end-members are present (Klovan and Imbrie, 1971; Klovan and Miesch, 1976; Miesch, 1976). These algorithms have also been modified to deduce end-members external to the measured data (Full et al., 1981) and have been used to model accurately the source rocks of heavy mineral assemblages through time (Stattegger, 1987, 1991). These methods could be also be applied to detrital geochronology in the future to model the provenance evolution in complex or poorly understood geological situations.

6. CONCLUSIONS

With the increasingly routine acquisition of large sets of geochronological data, in particular for provenance studies, an objective and quantitative method for describing and assessing this data must be established. Traditional assessment of age data has relied on the simple visual comparison of binned histograms with each other or expected protosources and is vulnerable to interpretation bias, especially as the number of sets of data increases. The adaptation of standard PCA methods has been implemented on data comprising 31 detrital samples

Quantitative comparison

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Fig. 12. Eastern coastal samples plotted using principal components I and II derived from zircon data and illustrating a distinct south-to-north trend along the coastline. Inset map illustrates sample locations along coastline. (inset) Probability density distributions along eastern coast also included for comparison.

across Australia with the following conclusions. Principal components were derived from the data itself and were readily interpreted using the known geological history of the region. In particular, the principal components were able to distinguish objectively between contributions from local Phanerozoic and exotic late Proterozoic provenances. This distinction was then used to clearly illustrate the provenance evolution along the eastern Australian coastline in a single visually insightful diagram. Although further work is possible in scrutinizing the assumptions involved in PCA, particularly the interpretation of component scores based on a priori knowledge, this methodology should have broad application in a variety of detrital geochronological settings. Acknowledgments—The author gratefully acknowledges the assistance and advice of W. Compston, I. S. Williams, and many others at the

Research School of Earth Sciences of the Australian National University during data acquisition. Some samples were supplied by S. Wollen and N. Gentle (RZM Pty Ltd; Hispanola, Hummock Hill Island, Robinvale, Spring Hill, and Tomago), M. Freeman (Department of Minerals and Energy, Western Australia; Eneabba, Minninup, Waroona), J. Smart (Wimmera Industrial Minerals; WIM 150), and N. Bassett (BHP Minerals; North Stradbroke Island). S. Pell and T. R. Ireland are thanked for permission to include their data. This article evolved greatly with many valuable comments from R. Stern, B. Davis, G. Bonham-Carter, J. Davis, G. Ross, and an anonymous reviewer. Geological Survey of Canada contribution number 1999/80. REFERENCES Acton F. S. (1970) Numerical Methods That Work. Harper & Row. Adams C. J. and Kelley S. (1998) Provenance of Permian-Triassic and Ordovician metagreywacke terranes in New Zealand: Evidence from 40 Ar/39Ar dating of detrital micas. Geologic. Soc. Am. Bull. 110, 422– 432.

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K. N. Sircombe

Aitchison J. (1986) The Statistical Analysis of Compositional Data. Chapman and Hall. Bowdler H., Martin R. S., Reisch C., and Wilkinson J. H. (1971) The QR and QL algorithms for symmetric matrices. In Handbook for Automatic Computation, v.2, Linear Algebra (ed. F. L. Bauer et al.), pp. 227–240. Brandon M. T. and Vance J. A. (1992) Tectonic evolution of the Cenozoic Olympic subduction complex, Washington State, as deduced from fission track ages for detrital zircons. Am. J. Sci. 292, 565– 636. Brown C. M. and Stephenson A. E. (1991) Geology of the Murray Basin Southeastern Australia. Bureau of Mineral Resources, Canberra, Bulletin 235. Bryan S. E., Constantine A. E., Stephens C. J., Ewart A., Scho¨n R. W., and Parianos J. (1997) Early Cretaceous volcano–sedimentary successions along the eastern Australian continental margin: Implications for the break-up of eastern Gondwana. Earth Planet. Sci. Lett. 153, 85–102. Chayes F. (1960) On correlation between variables of constant sum. J. Geophys. Res. 65, 4185– 4193. Chayes F. and Trochimczyk J. (1978) An effect of closure on the structure of principal components. Mathematic. Geol. 10, 323–333. Claoue´-Long J. C., Compston W., Roberts J., and Fanning C. M. (1995) Two Carboniferous ages: A comparison of SHRIMP zircon dating with conventional zircon ages and 40Ar/39Ar analysis. Geochronology time scales and global stratigraphic correlation. SEPM Special Publication 54, 1–21. Clemens K. E. and Komar P. D. (1988) Oregon beach-sand compositions produced by the mixing of sediments under a transgressing sea. J. Sediment. Petrol. 58, 519 –529. Colwell J. B. (1982) The nature and mineralogy of beach sands on the central and northern New South Wales and Southern Queensland coasts. Bureau of Mineral Resources, Canberra, Record 1982/1. Compston W. and Chappell B. W. (1979) Sr-isotope evolution of granitoid source rocks. In The Earth: Its Origin, Structure and Evolution (ed. M. W. McElhinny), pp. 377– 426. Academic Press. Compston W., Williams I. S., and Meyer C. (1984) U-Pb geochronology of zircons from lunar breccia 73217 using a Sensitive High Resolution Ion Microprobe. Proceeding of the 14th Lunar and Planetary Science Conference, Part 2. J. Geophys. Res. Suppl. 89, B525– B534. Coney P. J., Edwards A., Hine R., Morrison F., and Windram D. (1990) The regional tectonics of the Tasman orogenic system, eastern Australia. J. Structural Geol. 12, 519 –543. Connah T. H. (1961) Beach Sand Heavy Mineral Deposits of Queensland. Geological Survey of Queensland Publication 302. Dallmeyer R. D. and Takasu A. (1992) 40Ar/39Ar ages of detrital muscovite and whole-rock slate/phyllite, Narragansett Basin, RIMA, USA: Implications for rejuvenation during very low-grade metamorphism. Contrib. Mineral. Petrol. 110, 515–527. Davis J. C. (1986) Statistics and Data Analysis in Geology. John Wiley & Sons. Davis D. W., Pezzutto F., and Ojakangas R. W. (1990) The age and provenance of metasedimentary rocks in the Quetico Subprovince, Ontario, from single zircon analyses: Implications for Archean sedimentation and tectonics in the Superior Province. Earth Planet. Sci. Lett. 99, 195–205. Dodson M. H., Compston W., Williams I. S., and Wilson J. F. (1988) A search for ancient detrital zircons in Zimbabwean sediments. J. Geol. Soc., London 145, 977–983. Ewart A., Scho¨n R. W., and Chappell B. W. (1992) The Cretaceous volcanic–plutonic province of the central Queensland (Australia) coast—a rift related “calc-alkaline” province. Trans. Roy. Soc. Edinburgh: Earth Science 83, 327–345. Flood R. H. and Shaw S. E. (1977) Two “S-type” granite suites with low initial 87Sr/86Sr ratios from the New England Batholith, Australia. Contrib. Mineral. Petrol. 61, 161–173. Full W. E., Ehrlich R., and Klovan J. E. (1981) EXTENDED QMODEL—Objective definition of external end members in the analysis of mixtures. Mathematical Geol. 13, 331–344. Gardner D. E. (1955) Beach Sand Heavy Mineral Deposits of Eastern Australia. Bureau of Mineral Resources, Canberra, Bulletin 28. Gehrels G. E. and Dickinson W. R. (1995) Detrital zircon provenance

of Cambrian to Triassic miogeoclinal and eugeoclinal strata in Nevada. Am. J. Sci. 295, 18 – 48. Green D. C. (1973) Radiometric evidence of the Kanimblan Orogeny in southeastern Queensland and the age of the Neranleigh–Fernvale Group. J. Geol. Soc. Australia 20, 153–160. Golub G. H. and Van Loan C. F. (1983) Matrix Computations. John Hopkins University Press. Hails J. R. (1969) The nature and occurrence of heavy minerals in three coastal areas of New South Wales. J. Proceed. Roy. Soc. New South Wales 102, 21–39. Hurford A. J., Fitch F. J., and Clarke A. (1984) Resolution of the age structure of the detrital zircon populations of two Lower Cretaceous sandstones from the Weald of England by fission track dating. Geological Mag. 121, 269 –396. Ireland T. R. (1995) Ion microprobe mass spectrometry: Techniques and applications in cosmochemistry, geochemistry and geochronology. In Advances in Analytical Geochemistry (ed. M. Hyman and M. Row), pp. 1–118. JAI Press. Ireland T. R., Flo¨ttmann T., Fanning C. M., Gibson G. M., and Preiss W. V. (1998) Development of the early Paleozoic Pacific margin of Gondwana from detrital-zircon ages across the Delamerian orogen. Geology 26, 243–246. Klovan J. E. and Imbrie J. (1971) An algorithm and FORTRAN-IV program for large-scale Q-mode factor analysis and calculation of factor scores. Mathematical Geol. 3, 61–77. Klovan J. E. and Miesch A. T. (1976) Extended CABFAC and QMODEL computer programs for Q-mode factor analysis of compositional data. Computers and Geosciences 1, 161–178. Kucera M. and Malmgren B. A. (1998) Logratio transformation of compositional data—a resolution of the constant sum constraint. Marine Micropaleontol. 34, 117–120. Machado N., Schrank A., Noce C. M., and Gauthier G. (1996) Ages of detrital zircon from Archean-Paleoproterozoic sequences. Implications for greenstone belt setting and evolution of a Transamazonian foreland basin in Quadrilatero Ferrifero, Southeast Brazil. Earth Planet. Sci. Lett. 141, 259 –276. Manly B. F. J. (1994) Multivariate Statistical Methods, 2nd ed. Chapman and Hall. Martin R. S., Reisch C., and Wilkinson J. H. (1971) Householder’s tridiagonalization of a symmetric matrix. In Handbook for Automatic Computation, v.2, Linear Algebra (ed. F. L. Bauer et al.), pp. 212–226. Miesch A. T. (1976) Q-mode factor analysis of compositional data. Computers and Geosciences 1, 147–159. Montel J.-M., Foret S., Veschambre M., Nicollet C., and Provost A. (1996) Electron microprobe dating of monazite. Chem. Geol. 131, 37–53. Morton A. C., Claoue´-Long J. C., and Berge C. (1996) SHRIMP constraints on sediment provenance and transport history in the Mesozoic Statfjord Formation, North Sea. J. Geol. Soc., London 153, 915–929. Myers J. S. (1993) Precambrian history of the West Australian craton and adjacent orogens. Ann. Rev. Earth Planet. Sci. 21, 453– 485. Palfreyman W. D. (1984) Guide to the Geology of Australia. Bureau of Mineral Resources, Canberra, Bulletin 181. Payne R. W., Lane P. W., Ainsley A. E., Bicknell K. E., Digby P. G. N., Harding S. A., Leech P. K., Simpson H. R., Todd A. D., Verrier P. J., White R. P., Gower J. C., and Paterson L. J. (1993) Genstat 5 Release 3 Reference Manual. Clarendon Press. Pell S. D. (1994) The provenance of the Australian continental dunefields. Unpublished Ph.D. thesis, Australian National University, Canberra. Pell S. D., Williams I. S., and Chivas A. R. (1997) The use of protolith zircon-age fingerprints in determining the protosource areas for some Australian dunes sands. Sedimentary Geology 109, 233–260. Pirkle E. C., Pirkle F. L., Pirkle W. A., and Stayert P. R. (1984) The Yulee heavy mineral sands deposits. Economic Geology 79, 725– 737. Pirkle F. L., Pirkle E. C., Pirkle W. A., and Dicks S. E. (1985) Evaluation through correlation and principal component analysis of a delta origin for the Hawthorne and Citronelle sediments of Peninsular Florida. J. Geol. 93, 493–501.

Quantitative comparison Plumb K. A. (1979) The tectonic evolution of Australia. Earth Sci. Rev. 14, 205–249. Press W. H., Flannery B. P., Teukolsky S. A., and Vetterling W. T. (1988) Numerical Recipes in C. Cambridge University Press. Roy P. S. and Thom B. G. (1981) Late Quaternary marine deposition in New South Wales and southern Queensland—an evolutionary model. J. Geol. Soc. Australia 28, 471– 489. Roy P. S. and Thom B. G. (1991) Cainozoic shelf sedimentation model for the Tasman Sea margin of southeastern Australia. In The Cainozoic in Australia: A Re-appraisal of the Evidence (ed. M. A. J. William et al.), pp. 119 –136. Geological Society of Australia Special Publication 18. Sambridge M. S. and Compston W. (1994) Mixture modelling of multi-component data sets with application to ion-probe zircon ages. Earth Planet. Sci. Lett. 128, 373–390. Scheibner E. (1993) Tectonic setting. Geological Survey of New South Wales Memoir 12, 33– 46. Scott D. J. and Gauthier G. (1996) Comparison of TIMS (U-Pb) and laser ablation microprobe ICP-MS (Pb) techniques for age determination of detrital zircons from Paleoproterozoic metasedimentary rocks from northeastern Laurentia, Canada, with tectonic implications. Chemical Geology 131, 127–142. Shaw S. E. and Flood R. H. (1981) The New England Batholith, Eastern Australia: Geochemical variations in time and space. J. Geophys. Res. 86, 10530 –10544. Silverman B. W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall. Sircombe K. N. (1997) Detrital mineral SHRIMP geochronology and provenance analysis of sediments in eastern Australia. Unpublished Ph.D. thesis, Australian National University, Canberra. Sircombe K. N. (1999) Tracing provenance through the isotope ages of littoral and sedimentary detrital zircon, eastern Australia. Sedimentary Geology 124, 47– 67. Sircombe K. N. and Freeman M. (1999) Provenance of detrital zircon on the Western Australian coastline—implications for the geological history of the Perth Basin and denudation of the Yilgarn Craton. Geology 27, 879 – 882. Sircombe K. N. and McQueen K. G. (in press) Zircon dating of Devonian-Carboniferous rocks from the Bombala area, New South Wales. Aust. J. Earth Sci. Spry M. J., Gibson D. L., and Eggleton R. A. (1999) Tertiary evolution of the coastal lowlands and the Clyde River palaeovalley in southeast New South Wales. Australian J. Earth Sci. 46, 173–180. Stattegger K. (1987) Heavy mineral and provenance of sands: Modeling of lithological end members from river sands of northern Austria and from sandstones of the Austroalpine Gosau Formation (Late Cretaceous). J. Sedimentary Petrol. 57, 301–310. Stattegger K. (1991) Processes controlling the composition of heavymineral assemblages: Mixing, unmixing, and sediment-source relations. Geological Society of America, Abstracts with Programs 23, A107. Suzuki K. and Adachi M. (1991) Precambrian provenance and Silurian metamorphism of Tsubonosawa paragneiss in the South Kitakami terrane, Northeast Japan, revealed by the chemical Th-U-total Pb isochron ages of monazite, zircon and xenotime. Geochem. J. 25, 357–376. Tera F. and Wasserburg G. J. (1972) U-Th-Pb systematics in three Apollo 14 basalts and the problem of initial Pb in lunar rocks. Earth Planet. Sci. Lett. 14, 281–304. Tera F. and Wasserburg G. J. (1974) U-Th-Pb systematics in lunar rocks and inferences about lunar evolution and the age of the moon. Proceedings 5th Lunar Science Conference 2, 1571–1599. Turner S. P., Adams C. J., Flo¨ttmann T., and Foden J. D. (1993) Geochemical and geochronological constraints on the Glenelg River Complex, western Victoria. Australian J. Earth Sci. 40, 275–292. Turner S. P., Kelley S. P., VandenBerg A. H. M., Foden J. D., Sandiford M., and Flo¨ttmann T. (1996) Source of the Lachlan fold belt flysch linked to convective removal of the lithospheric mantle and rapid exhumation of the Delamerian-Ross fold belt. Geology 24, 941–944. Veevers J. J. (1984) Phanerozoic Earth History of Australia. Claredon Press. Wackernagel H. (1995) Multivariate Geostatistics. Springer-Verlag.

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Wagreich M. and Marschalko R. (1995) Late Cretaceous to Early Tertiary palaeogeography of the Western Carpathians (Slovakia) and the Eastern Alps (Austria): Implications from heavy minerals. Geologishe Rundschau 84, 187–199. Wetherill G. W. (1956) Discordant Uranium-Lead Ages, I. Transactions, American Geophysical Union 37, 320 –326. Wetherill G. W. (1963) Discordant uranium-lead ages, Part 2: Discordant ages resulting from diffusion of lead and uranium. J. Geophys. Res. 68, 2957–2965. Whitehouse M. J., Claesson S., Sunde T., and Vestin J. (1997) Ion microprobe U-Pb zircon geochronology and correlation of Archean gneisses from Lewisian Complex of Gruinard Bay, northwestern Scotland. Geochim. Cosmochim. Acta 61, 4429 – 4438. Whitworth H. F. (1959) The zircon-rutile deposits on the beaches of the east coast of Australia with special reference to their mode of occurrence and the origin of the minerals. Technical Reports, Department of Mines, New South Wales 4, 7– 60. Williams I. S. (1992) Some observations on the use of zircon U-Pb geochronology in the study of granitic rocks. Transactions of the Royal Society of Edinburgh: Earth Sciences 83, 447– 458. Williams I. S., Compston W., and Chappell B. W. (1983) Zircon and monazite U-Pb systems and the histories of I-type magmas, Berridale batholith, Australia. J. Petrol. 24, 76 –97. Williams I. S., Chappell B. W., McCulloch M. T., and Crook K. A. W. (1991) Inherited and detrital zircon—Clues to the early growth of crust in the Lachlan fold belt. Geological Society of Australia Abstracts 29, 58. Williams I. S., Chappell B. W., Crook K. A. W., and Nicoll R. S. (1994) In search of the provenance of the Early Palaeozoic flysch in the Lachlan fold belt, southeastern Australia. Geological Society of Australia Abstracts 37, 464. Williams V. A. (1990) WIM 150 detrital heavy mineral deposit. In Geology of the Mineral Deposits of Australia and Papua New Guinea (ed. F. E. Hughes), pp. 1609 –1614. The Australasian Institute of Mining and Metallurgy. Wysoczanski R. J., Gibson G. M., and Ireland T. R. (1997) Detrital zircon age patterns and provenance in late Paleozoic– early Mesozoic New Zealand terranes and development of the paleo-Pacific Gondwana margin. Geology 25, 939 –942. APPENDIX Log-ratio Transformation of Proportional Data To avoid closure effects proportional data can be transformed using the method described by Aitchison (1986):

冉冊 x ij gi

x ij⬘ ⫽ 1n

(3)

where xij⬘ is the transformed proportion j of sample i. The denominator gi is the geometric mean of the percentage proportions of sample i given by:

冑写 n

gi ⫽

n

xi

(4)

i⫽1

However, zero values will be present in many sets of proportional data rendering a direct log-ratio transform meaningless. Aitchison (1986, p. 268) provides a method to work around this problem by assuming that zero values can be replaced by the maximum rounding-off error ␦ before log-ratio transformation (e.g., 0.005% if proportions are recorded to two decimal places). If a set of proportional data has C zero value and D–C non-zero value components, then the zero value components become:

␦

共C ⫹ 1兲共D ⫺ C兲 D2

Positive components are reduced by:

(5)

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␦

C共C ⫹ 1兲 D2

(6)

Synopsis of Principal Component Analysis Method Principal components for data with p variables are derived from the sample variance– covariance matrix:

C⫽

冤

c 11 c 21 · · · c p1

c 12 c 22 · · · c p2

··· ··· ·· · ···

c 1p c 2p · · · c pp

冥

(7)

where the diagonal element cii is the variance of Xi, as given by:

冘 n

s i2 ⫽

共 x ij ⫺ x៮ i兲 2/共 p ⫺ 1兲

(8)

i⫽1

Z i ⫽ a i1X 1 ⫹ a i2 X 2 ⫹ . . . ⫹ a ip X p

and nondiagonal elements cij are sample covariances between variables Xi and Xj, as given by:

冘 n

c jk ⫽

共 x ij ⫺ x៮ j兲共 x ik ⫺ x៮ k兲/共 p ⫺ 1兲

(9)

i⫽1

A correlation matrix can also be used if it is desirable to avoid one variable having too great an influence on the resultant principal components (e.g., Manly, 1994). This is typically done when a comparison between variables with different measurement units is required. However, in such a matrix, the information about the variance within the variables is lost and this approach has not been used here. Principal components are derived from the eigenvalues and eigenvectors of the sample variance– covariance matrix: 关C兴关 x兴 i ⫽ ␭ i关 x兴 i

latent roots or eigenvalues of matrix [C]. Because the matrix is symmetrical, the eigenvectors are orthogonal to each other, and thus are uncorrelated. The calculation of eigenvalues and eigenvectors is a nontrivial task involving, at the simplest level, the roots of the characteristic polynomial of the matrix determinant. As the size of the matrix increases, matrix transformations such as Jacobi or QL algorithms are more efficient ways to calculate eigenvalues and eigenvectors. No brief or “easy to implement” description is possible within the scope of this article and interested readers are referred to such texts as Acton (1970), Golub and Van Loan (1983), and Press et al. (1988). The algorithms used in this article were derived from the tred2 and tql2 subroutines (Bowdler et al., 1971; Martin et al., 1971), which transforms a real symmetric matrix (the variance– covariance matrix) into a tridiagonal matrix, which in turn is used to calculate the eigenvalues and eigenvectors using a QL algorithm. A principal component is described in terms of the variables it supersedes, for example,

i ⫽ 1,2, . . . , p

(10)

where [C] is the p-by-p variance– covariance matrix, [x]i is the eigenvector related to the scalar ␭i, which has particular values that are the

(11)

where the variance of Zi equals the eigenvalue ␭i. An important property of this process is that the sum of the eigenvalues equals the sum of the diagonal elements (trace) of matrix [C]; thus, the total variance of the principal components is equal to the total variance of the original variables. The values ai1,ai2, . . . ,aip are contained in the corresponding eigenvector xi and are limited by: a i12 ⫹ a i22 ⫹ . . . ⫹ a ip2 ⫽ 1

(12)

In effect, ai1, ai2, . . . ,aip describe the contribution or loading each of the variables Xi has on principal component Zi. The eigenvectors are used to calculate the score an individual sample has for each principal component: 关S兴 ⫽ 关D兴关a兴

(13)

where [D] is the log-ratio transformed data matrix of n samples by p variables, [a] is the p-by-p matrix of eigenvectors, and [S] is n by p matrix of sample scores for each principal component.